Hermite 矩阵特征值分解的硬件加速

In the field of digital signal processing, the eigenvalue decomposition of Hermitian matrices possesses a very wide range of applications. To solve the problem of its hardware implementation, a hardware acceleration architecture was proposed based on Jacobi algorithm in complex domain, and the design scheme was arranged to be applied to Hermite matrices with different sizes. In order to achieve a balance among calculation accuracy, calculation speed and resource occupancy, the quantization bit width of the fixed-point operation was simulated on the Matlab platform firstly. Taking the Hermite matrix of size 8×8 as an example, the quantization of 15-bit decimal places was determined as the best. Then, the hardware circuit structure was introduced respectively for finding the largest off-diagonal element, constructing unitary matrix and updating eigenvalue matrix and eigenvector matrix in hardware acceleration of Jacobi algorithm for complex number domain. Finally, the hardware acceleration method was implemented on the Zynq-7000 series FPGA development board, taking only 17 438 LUTs and 24 650 Registers to complete the eigenvalue decomposition of an 8×8 Hermite matrix in 34.42 μs.